It is part of a group of macroraptorial sperm whales that all share several features for hunting large prey, such as deeply rooted and thick teeth.

Because of its short pointed snout and strongly curved front teeth, it probably fed on the marine vertebrates of its time, such as seals and other whales.

[1] The type species, A. deinodon, was described in 2008 by Olivier Lambert, Giovanni Bianucci and Christian De Muizon from a skull, catalogued MNHN SAS 1626, discovered in the Sud-Sacaco locality.

Later, a second A. deinodon specimen consisting of a right parietal bone was recovered from the Aguada de Lomas locality and recorded as MNHM F-PPI 272.

The rocks at Aguada de Lomas are younger than both previously mentioned localities, and the specimen was dated to the Messinian stage of the Miocene, 6.9–6.7 mya.

[1] A third Acrophyseter skull, catalogued MUSM 2182, was discovered in the Cerro los Quesos locality, dating from the same period as Aguada de Lomas.

[2] The species name robustus comes from Latin and references the thick bone constituting the edges of the supracranial basin and the base of the rostrum.

This suggests a different feeding strategy from modern sperm whales, which all use suction-feeding due to a lack of teeth in the upper jaw.

[1] Discovered along the tooth sockets were buccal exostoses: bony growths which may have developed during biting to strengthen the teeth, acting as buttresses.

The supracranial basin, in turn, overhangs the orbit around the eye but does not extend onto the snout, unlike in other macroraptorial sperm whales.

Physeteridae Kogiidae Features like the short, pointed snout, and robust, curved front teeth suggest that Acrophyseter targeted large prey.

[2] The localities of the Pisco Formation where remains of the animal have been found have yielded the remains of numerous marine vertebrates: the whales Piscolithax and Piscobalaena, the dolphins Brachydelphis, Atocetus iquensis, and Belonodelphis, the seal Acrophoca, the penguins Spheniscus urbinai and Spheniscus muizoni, the marine sloth Thalassocnus natans, the crocodile Piscogavialis, and the megalodon and broad-toothed mako sharks (Cosmopolitodus hastalis).